Theorem. (
t48_ordinal3)
∀m1_subset_1 : set → set → prop, ∀k1_zfmisc_1 : set → set, ∀k1_xboole_0 : set, ∀v1_ordinal1 : set → prop, ∀v2_ordinal1 : set → prop, ∀esk5_0 : set, ∀esk3_0 : set, ∀esk4_0 : set, ∀esk2_0 : set, ∀esk10_0 : set, ∀esk1_0 : set, ∀esk11_0 : set, ∀o_0_0_xboole_0 : set, ∀esk7_0 : set, ∀esk8_0 : set, ∀esk6_1 : set → set, ∀esk9_0 : set, ∀esk12_0 : set, ∀v5_ordinal1 : set → prop, ∀v6_ordinal1 : set → prop, ∀v7_ordinal1 : set → prop, ∀r1_tarski : set → set → prop, ∀r1_ordinal1 : set → set → prop, ∀v1_xboole_0 : set → prop, ∀esk13_2 : set → set → set, ∀r2_hidden : set → set → prop, ∀k11_ordinal2 : set → set → set, ∀k10_ordinal2 : set → set → set, ∀v3_ordinal1 : set → prop, (∀X1 X2 X3, ((k10_ordinal2 (k11_ordinal2 X1 X3) (k11_ordinal2 X2 X3)) = (k11_ordinal2 (k10_ordinal2 X1 X2) X3) → False) → v3_ordinal1 X3 → v3_ordinal1 X2 → v3_ordinal1 X1 → False) → (∀X1 X2 X3, ((k10_ordinal2 (k10_ordinal2 X1 X2) X3) = (k10_ordinal2 X1 (k10_ordinal2 X2 X3)) → False) → v3_ordinal1 X3 → v3_ordinal1 X2 → v3_ordinal1 X1 → False) → (∀X1 X2, ((k10_ordinal2 X2 (esk13_2 X2 X1)) = X1 → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → r2_hidden X2 X1 → False) → (∀X2 X1 X3, (m1_subset_1 X1 X3 → False) → r2_hidden X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X3) → False) → (∀X1 X2 X3, (X2 = X3 → False) → (k10_ordinal2 X1 X2) = (k10_ordinal2 X1 X3) → v3_ordinal1 X3 → v3_ordinal1 X2 → v3_ordinal1 X1 → False) → (∀X1 X2, (v3_ordinal1 (esk13_2 X1 X2) → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → r2_hidden X1 X2 → False) → (∀X2 X1 X3, v1_xboole_0 X3 → r2_hidden X1 X2 → m1_subset_1 X2 (k1_zfmisc_1 X3) → False) → (∀X1 X2, (esk13_2 X1 X2) = k1_xboole_0 → v3_ordinal1 X2 → v3_ordinal1 X1 → r2_hidden X1 X2 → False) → (∀X1 X2, (X2 = k1_xboole_0 → False) → (r1_ordinal1 X1 (k11_ordinal2 X1 X2) → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → False) → (∀X1 X2, (X2 = k1_xboole_0 → False) → (r1_ordinal1 X1 (k11_ordinal2 X2 X1) → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → False) → (∀X2 X1, (r1_ordinal1 X1 (k10_ordinal2 X1 X2) → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → False) → (∀X2 X1, (r1_ordinal1 X1 (k10_ordinal2 X2 X1) → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → False) → (∀X1 X2, (r1_tarski X1 X2 → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → r1_ordinal1 X1 X2 → False) → (∀X1 X2, (r1_ordinal1 X1 X2 → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → r1_tarski X1 X2 → False) → (∀X2 X1, (r1_tarski X1 X2 → False) → m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → (∀X2 X1, (X1 = X2 → False) → (r2_hidden X2 X1 → False) → (r2_hidden X1 X2 → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → False) → (∀X1 X2, r2_hidden X1 X2 → r1_tarski X2 X1 → False) → (∀X2 X1, r2_hidden X2 X1 → r2_hidden X1 X2 → False) → (∀X2 X1, (v7_ordinal1 (k10_ordinal2 X1 X2) → False) → v7_ordinal1 X2 → v7_ordinal1 X1 → False) → (∀X2 X1, (v3_ordinal1 (k10_ordinal2 X1 X2) → False) → v7_ordinal1 X2 → v7_ordinal1 X1 → False) → (∀X2 X1, (v3_ordinal1 (k10_ordinal2 X1 X2) → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → False) → (∀X2 X1, (v3_ordinal1 (k11_ordinal2 X1 X2) → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → False) → (∀X1 X2, (v6_ordinal1 X2 → False) → v6_ordinal1 X1 → m1_subset_1 X2 (k1_zfmisc_1 X1) → False) → (∀X2 X1, (r1_ordinal1 X2 X1 → False) → (r1_ordinal1 X1 X2 → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → False) → (∀X2 X1, (m1_subset_1 X1 (k1_zfmisc_1 X2) → False) → r1_tarski X1 X2 → False) → (∀X1 X2, (v1_xboole_0 X2 → False) → (r2_hidden X1 X2 → False) → m1_subset_1 X1 X2 → False) → (∀X2 X1, (m1_subset_1 X1 X2 → False) → r2_hidden X1 X2 → False) → (∀X1 X2, (v3_ordinal1 X2 → False) → v3_ordinal1 X1 → m1_subset_1 X2 X1 → False) → (∀X1 X2, (v3_ordinal1 X2 → False) → v3_ordinal1 X1 → m1_subset_1 X2 X1 → False) → (∀X1 X2, v1_xboole_0 X2 → r2_hidden X1 X2 → False) → (∀X2 X1, (r1_ordinal1 X1 X1 → False) → v3_ordinal1 X2 → v3_ordinal1 X1 → False) → (∀X1, (v3_ordinal1 X1 → False) → v1_ordinal1 X1 → v2_ordinal1 X1 → False) → (∀X2 X1, (X1 = X2 → False) → v1_xboole_0 X2 → v1_xboole_0 X1 → False) → (∀X1, (v7_ordinal1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v5_ordinal1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v2_ordinal1 X1 → False) → v3_ordinal1 X1 → False) → (∀X1, (v1_ordinal1 X1 → False) → v3_ordinal1 X1 → False) → (∀X1, (v6_ordinal1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (v3_ordinal1 X1 → False) → v7_ordinal1 X1 → False) → (∀X1, (v3_ordinal1 X1 → False) → v1_xboole_0 X1 → False) → (∀X1, (X1 = k1_xboole_0 → False) → v1_xboole_0 X1 → False) → (esk4_0 = esk2_0 → esk5_0 = esk3_0 → False) → (v1_xboole_0 esk12_0 → False) → (v1_xboole_0 esk10_0 → False) → (v1_xboole_0 esk9_0 → False) → (((k10_ordinal2 (k11_ordinal2 esk4_0 esk1_0) esk5_0) = (k10_ordinal2 (k11_ordinal2 esk2_0 esk1_0) esk3_0) → False) → False) → (∀X1, (m1_subset_1 (esk6_1 X1) X1 → False) → False) → (∀X1, (r1_tarski X1 X1 → False) → False) → ((r2_hidden esk5_0 esk1_0 → False) → False) → ((r2_hidden esk3_0 esk1_0 → False) → False) → ((v7_ordinal1 esk12_0 → False) → False) → ((v7_ordinal1 esk11_0 → False) → False) → ((v1_xboole_0 esk8_0 → False) → False) → ((v1_xboole_0 o_0_0_xboole_0 → False) → False) → ((v1_xboole_0 k1_xboole_0 → False) → False) → ((v2_ordinal1 esk9_0 → False) → False) → ((v1_ordinal1 esk9_0 → False) → False) → ((v3_ordinal1 esk9_0 → False) → False) → ((v3_ordinal1 esk7_0 → False) → False) → ((v3_ordinal1 esk5_0 → False) → False) → ((v3_ordinal1 esk4_0 → False) → False) → ((v3_ordinal1 esk3_0 → False) → False) → ((v3_ordinal1 esk2_0 → False) → False) → ((v3_ordinal1 esk1_0 → False) → False) → ((o_0_0_xboole_0 = k1_xboole_0 → False) → False) → False